Molarity, Molalility question

40.0 g of a solute is dissolved in 500. mL of a solvent to give a solution with a volume of 495 mL. The solvent has a density of 1.00 g/mL. Which statement about this solution is correct?


A. The molarity and molality cannot be compared without knowing the solute.
B. The molarity is greater than the molality.
C. The molarity is the same as the molality.
D. The molarity and molality cannot be compared without knowing the density of the solution as well.
E. The molarity is lower than the molality.


The answer is B, but why

OK, there is 40.0 g in both, so moles are constant, forget about them.

molarity is moles solute / total volume of solution

Molarity = moles / 0.495 L


molality is moles solute / mass of solvent only
mass solvent added = volume x density = 500 ml x 1.00 g/ml = 500 g = 0.500 kg

molality = moles / 0.500 kg


So for molarity we divide moles by 0.495 and for molality we divide the same number of moles by 0.500
resulting in molarity being the higher value...

eg
1 / 0.495 = 2.02
1 /0.500 = 2.00


Careful with reading the wording in questions like these. If you had been given the total volume of the solution to start with rather then the volume of solvent added to the 40.0 g the answer would be the opposite.